Identification and inference for marginal average treatment effect on the treated with an instrumental variable

Lan Liu, Wang Miao, Baoluo Sun, James Robins, Eric Tchetgen Tchetgen

Research output: Contribution to journalArticlepeer-review


In observational studies, treatments are typically not randomized and, therefore, estimated treatment effects may be subject to a confounding bias. The instrumental variable (IV) design plays the role of a quasi-experimental handle because the IV is associated with the treatment and only affects the outcome through the treatment. In this paper, we present a novel framework for identification and inferences, using an IV for the marginal average treatment effect amongst the treated (ETT) in the presence of unmeasured confounding. For inferences, we propose three semiparametric approaches: (i) an inverse probability weighting (IPW); (ii) an outcome regression (OR); and (iii) a doubly robust (DR) estimation, which is consistent if either (i) or (ii) is consistent, but not necessarily both. A closed-form locally semiparametric efficient estimator is obtained in the simple case of a binary IV, and outcome, and the efficiency bound is derived for the more general case.

Original languageEnglish (US)
Pages (from-to)1517-1541
Number of pages25
JournalStatistica Sinica
Issue number3
StatePublished - Jul 2020

Bibliographical note

Funding Information:
The content is solely the responsibility of the authors. Lan Liu was supported by NSF DMS 1916013. Professor Eric Tchetgen Tchetgen was supported by R01 AI032475, R21 AI113251, R01 ES020337, and R01 AI104459. Wang Miao was supported by the China Scholarship Council.


  • Counterfactuals
  • Double robustness
  • Effect of treatment on the treated
  • Instrumental variable
  • Unmeasured confounding

PubMed: MeSH publication types

  • Journal Article

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